The evolution and distribution of temperature have been studied theoretically for an idealized model of a four‐ball wear‐test apparatus which can be used to study macroscopic effects of surfaces interacting under frictional conditions. The finite‐difference method was used to solve the coupled equations of heat generation, conduction, and cooling. Parameters were chosen to represent two types of material, a typical steel with relatively good thermal conductivity, and a ceramic with relatively poor thermal conductivity. Two values for the coefficients of friction were used to simulate dry and lubricated surfaces. A significant dependence on thermal conductivity was found.